scholarly journals Single-Machine Scheduling Problems with a Sum-of-Processing-Time-Based Learning Function

2009 ◽  
Vol 2009 ◽  
pp. 1-8
Author(s):  
Xingong Zhang ◽  
Guangle Yan
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Completion Time ◽  
Processing Time ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Proposed Model ◽  
Time Minimization ◽  
Polynomially Solvable

Recently, learning scheduling problems have received increasing attention. However, the majority of the research assume that the actual job processing time is a function of its position. This paper deals with the single-machine scheduling problem with a sum-of-processing-time-based learning effect. By the effect of sum-of-processing-time-based learning, we mean that the processing time of a job is defined by total normal processing time of jobs in front of it in the sequence. We show that the single-machine makespan problem remains polynomially solvable under the proposed model. We show that the total completion time minimization problem for a≥1 remains polynomially solvable under the proposed model. For the case of 0<a<1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times.

A Note on Single-Machine Scheduling with Deteriorating Jobs

2011 ◽  
Vol 219-220 ◽  
pp. 483-486
Author(s):  
Yun Qiang Yin ◽  
Feng Lian Yuan
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Optimal Schedule ◽  
Real Life ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Proposed Model ◽  
Time Minimization ◽  
Polynomially Solvable ◽  
Job Deterioration

In many real life applications, jobs deteriorate at a certain rate while waiting to be processed. This paper introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. We show that the single-machine makespan minimization problem remains polynomially solvable under the proposed model. We also show that an optimal schedule of the total completion time minimization problem is polynomially solvable under some cases and-shaped with respect to job deterioration rates for other cases.

Single Machine Two-Agent Scheduling with Deteriorating Jobs

2016 ◽  
Vol 33 (05) ◽  
pp. 1650034 ◽  
Author(s):  
Zhenyou Wang ◽  
Cai-Min Wei ◽  
Yu-Bin Wu
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Agent Scheduling ◽  
Polynomially Solvable ◽  
Weighted Completion Time

This paper deals with the single machine scheduling problem with deteriorating jobs in which there are two distinct families of jobs (i.e., two-agent) pursuing different objectives. In this model the processing time of a job is defined as a function that is proportional to a linear function of its stating time. For the following three scheduling criteria: minimizing the makespan, minimizing the total weighted completion time, and minimizing the maximum lateness, we show that some basic versions of the problem are polynomially solvable. We also establish the conditions under which the problem is computationally hard.

Robust Single Machine Scheduling with Stochastic Processing Times Based on Event Point

2014 ◽  
Vol 668-669 ◽  
pp. 1641-1645
Author(s):  
Xiao Xia He ◽  
Chun Yao ◽  
Qiu Hua Tang
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Model Base ◽  
Processing Times ◽  
Robust Model ◽  
Stochastic Processing ◽  
Stochastic Processing Times

The scheduling of the single machine is of major importance in applications. The focus of this work is to analyze the scheduling problems in single-machine scheduling in the presence of uncertain parameters. By assuming that the processing time is represented by the nominal value plus a perturbation, we propose a robust model base on event point, and we obtain the feasible job sequence with some probability confidence level.

SINGLE MACHINE SCHEDULING WITH A LEARNING EFFECT AND A RATE-MODIFYING ACTIVITY

2011 ◽  
Vol 28 (04) ◽  
pp. 511-521 ◽  
Author(s):  
CHUANLI ZHAO ◽  
HENGYONG TANG
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Learning Effect ◽  
Window Size ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Polynomial Time Algorithms ◽  
Due Window ◽  
Machine Scheduling Problems

In the paper, single machine scheduling problems with a learning effect and a rate-modifying activity are considered. Under the learning effect, the processing time of a job is a decreasing function of its position in the sequence. The rate-modifying activity is an event that can change the speed of the machine, and hence the processing time of jobs after the activity. The following objective functions are considered: the makespan, the total earliness, tardiness and completion time penalty, and the total earliness, tardiness, due-window starting time and due-window size penalty. Polynomial time algorithms are proposed to optimally solve the problems.

SINGLE MACHINE SCHEDULING WITH LINEAR DETERIORATING JOBS UNDER PREDICTIVE DISRUPTION

2011 ◽  
Vol 28 (03) ◽  
pp. 419-429 ◽  
Author(s):  
CHUAN-LI ZHAO ◽  
HENG-YONG TANG
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Optimal Schedule ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Completion Time ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Original Objective

This paper considers single machine scheduling problems with linear deteriorating jobs under predictive disruption. In this model, the actual processing time of a job is a increasing linear function of its starting time; and machine is subject to an availability constraint. We assume that an optimal schedule can be obtained by using some algorithms if machine is available at all time. Because of the machine disruption, the original schedule may become infeasible or too far from optimal. We want to create the new schedule that takes into account both the original objective function and a measure of deviation from the original schedule. We consider two versions of the problem. In the first one, the objective is weighted sum of total completion time and total tardiness while in the second one, the objective is weighted sum of total completion time and total earliness. We first prove some properties of the optimal schedule then dynamic programming algorithms are proposed, respectively.

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